Integrand size = 106, antiderivative size = 24 \[ \int \frac {-24 e^{5 x}+e^{2+e^{2-5 x} x^3} \left (-24 x^2+40 x^3\right )}{e^{5 x+2 e^{2-5 x} x^3}+e^{5 x+e^{2-5 x} x^3} (6 x+6 \log (2))+e^{5 x} \left (9 x^2+18 x \log (2)+9 \log ^2(2)\right )} \, dx=\frac {8}{e^{e^{2-5 x} x^3}+3 (x+\log (2))} \]
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Time = 0.27 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.96, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6820, 6818} \[ \int \frac {-24 e^{5 x}+e^{2+e^{2-5 x} x^3} \left (-24 x^2+40 x^3\right )}{e^{5 x+2 e^{2-5 x} x^3}+e^{5 x+e^{2-5 x} x^3} (6 x+6 \log (2))+e^{5 x} \left (9 x^2+18 x \log (2)+9 \log ^2(2)\right )} \, dx=\frac {8}{e^{e^{2-5 x} x^3}+3 x+\log (8)} \]
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Rule 6818
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{-5 x} \left (-24 e^{5 x}+8 e^{2+e^{2-5 x} x^3} x^2 (-3+5 x)\right )}{\left (e^{e^{2-5 x} x^3}+3 x+\log (8)\right )^2} \, dx \\ & = \frac {8}{e^{e^{2-5 x} x^3}+3 x+\log (8)} \\ \end{align*}
Time = 0.16 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.96 \[ \int \frac {-24 e^{5 x}+e^{2+e^{2-5 x} x^3} \left (-24 x^2+40 x^3\right )}{e^{5 x+2 e^{2-5 x} x^3}+e^{5 x+e^{2-5 x} x^3} (6 x+6 \log (2))+e^{5 x} \left (9 x^2+18 x \log (2)+9 \log ^2(2)\right )} \, dx=\frac {8}{e^{e^{2-5 x} x^3}+3 x+\log (8)} \]
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Time = 0.43 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00
method | result | size |
risch | \(\frac {8}{3 \ln \left (2\right )+3 x +{\mathrm e}^{x^{3} {\mathrm e}^{-5 x +2}}}\) | \(24\) |
norman | \(\frac {8}{3 \ln \left (2\right )+3 x +{\mathrm e}^{x^{3} {\mathrm e}^{2} {\mathrm e}^{-5 x}}}\) | \(28\) |
parallelrisch | \(\frac {8}{3 \ln \left (2\right )+3 x +{\mathrm e}^{x^{3} {\mathrm e}^{2} {\mathrm e}^{-5 x}}}\) | \(28\) |
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Time = 0.26 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.62 \[ \int \frac {-24 e^{5 x}+e^{2+e^{2-5 x} x^3} \left (-24 x^2+40 x^3\right )}{e^{5 x+2 e^{2-5 x} x^3}+e^{5 x+e^{2-5 x} x^3} (6 x+6 \log (2))+e^{5 x} \left (9 x^2+18 x \log (2)+9 \log ^2(2)\right )} \, dx=\frac {8 \, e^{\left (5 \, x\right )}}{3 \, {\left (x + \log \left (2\right )\right )} e^{\left (5 \, x\right )} + e^{\left ({\left (x^{3} e^{2} + 5 \, x e^{\left (5 \, x\right )}\right )} e^{\left (-5 \, x\right )}\right )}} \]
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Time = 0.10 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {-24 e^{5 x}+e^{2+e^{2-5 x} x^3} \left (-24 x^2+40 x^3\right )}{e^{5 x+2 e^{2-5 x} x^3}+e^{5 x+e^{2-5 x} x^3} (6 x+6 \log (2))+e^{5 x} \left (9 x^2+18 x \log (2)+9 \log ^2(2)\right )} \, dx=\frac {8}{3 x + e^{x^{3} e^{2} e^{- 5 x}} + 3 \log {\left (2 \right )}} \]
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Time = 0.30 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.96 \[ \int \frac {-24 e^{5 x}+e^{2+e^{2-5 x} x^3} \left (-24 x^2+40 x^3\right )}{e^{5 x+2 e^{2-5 x} x^3}+e^{5 x+e^{2-5 x} x^3} (6 x+6 \log (2))+e^{5 x} \left (9 x^2+18 x \log (2)+9 \log ^2(2)\right )} \, dx=\frac {8}{3 \, x + e^{\left (x^{3} e^{\left (-5 \, x + 2\right )}\right )} + 3 \, \log \left (2\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 621 vs. \(2 (23) = 46\).
Time = 0.30 (sec) , antiderivative size = 621, normalized size of antiderivative = 25.88 \[ \int \frac {-24 e^{5 x}+e^{2+e^{2-5 x} x^3} \left (-24 x^2+40 x^3\right )}{e^{5 x+2 e^{2-5 x} x^3}+e^{5 x+e^{2-5 x} x^3} (6 x+6 \log (2))+e^{5 x} \left (9 x^2+18 x \log (2)+9 \log ^2(2)\right )} \, dx=\frac {8 \, {\left (15 \, x^{5} e^{\left (5 \, x + 2\right )} + 30 \, x^{4} e^{\left (5 \, x + 2\right )} \log \left (2\right ) + 15 \, x^{3} e^{\left (5 \, x + 2\right )} \log \left (2\right )^{2} + 5 \, x^{4} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} - 9 \, x^{4} e^{\left (5 \, x + 2\right )} + 5 \, x^{3} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} \log \left (2\right ) - 18 \, x^{3} e^{\left (5 \, x + 2\right )} \log \left (2\right ) - 9 \, x^{2} e^{\left (5 \, x + 2\right )} \log \left (2\right )^{2} - 3 \, x^{3} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} - 3 \, x^{2} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} \log \left (2\right ) + 3 \, x e^{\left (10 \, x\right )} + 3 \, e^{\left (10 \, x\right )} \log \left (2\right ) + e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 10 \, x\right )}\right )}}{45 \, x^{6} e^{\left (5 \, x + 2\right )} + 135 \, x^{5} e^{\left (5 \, x + 2\right )} \log \left (2\right ) + 135 \, x^{4} e^{\left (5 \, x + 2\right )} \log \left (2\right )^{2} + 45 \, x^{3} e^{\left (5 \, x + 2\right )} \log \left (2\right )^{3} + 30 \, x^{5} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} - 27 \, x^{5} e^{\left (5 \, x + 2\right )} + 60 \, x^{4} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} \log \left (2\right ) - 81 \, x^{4} e^{\left (5 \, x + 2\right )} \log \left (2\right ) + 30 \, x^{3} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} \log \left (2\right )^{2} - 81 \, x^{3} e^{\left (5 \, x + 2\right )} \log \left (2\right )^{2} - 27 \, x^{2} e^{\left (5 \, x + 2\right )} \log \left (2\right )^{3} + 5 \, x^{4} e^{\left (2 \, x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} - 18 \, x^{4} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} + 5 \, x^{3} e^{\left (2 \, x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} \log \left (2\right ) - 36 \, x^{3} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} \log \left (2\right ) - 18 \, x^{2} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} \log \left (2\right )^{2} - 3 \, x^{3} e^{\left (2 \, x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} - 3 \, x^{2} e^{\left (2 \, x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} \log \left (2\right ) + 9 \, x^{2} e^{\left (10 \, x\right )} + 18 \, x e^{\left (10 \, x\right )} \log \left (2\right ) + 9 \, e^{\left (10 \, x\right )} \log \left (2\right )^{2} + 6 \, x e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 10 \, x\right )} + 6 \, e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 10 \, x\right )} \log \left (2\right ) + e^{\left (2 \, x^{3} e^{\left (-5 \, x + 2\right )} + 10 \, x\right )}} \]
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Timed out. \[ \int \frac {-24 e^{5 x}+e^{2+e^{2-5 x} x^3} \left (-24 x^2+40 x^3\right )}{e^{5 x+2 e^{2-5 x} x^3}+e^{5 x+e^{2-5 x} x^3} (6 x+6 \log (2))+e^{5 x} \left (9 x^2+18 x \log (2)+9 \log ^2(2)\right )} \, dx=\int -\frac {24\,{\mathrm {e}}^{5\,x}+{\mathrm {e}}^{x^3\,{\mathrm {e}}^{-5\,x}\,{\mathrm {e}}^2}\,{\mathrm {e}}^2\,\left (24\,x^2-40\,x^3\right )}{{\mathrm {e}}^{5\,x}\,\left (9\,x^2+18\,\ln \left (2\right )\,x+9\,{\ln \left (2\right )}^2\right )+{\mathrm {e}}^{5\,x}\,{\mathrm {e}}^{2\,x^3\,{\mathrm {e}}^{-5\,x}\,{\mathrm {e}}^2}+{\mathrm {e}}^{5\,x}\,{\mathrm {e}}^{x^3\,{\mathrm {e}}^{-5\,x}\,{\mathrm {e}}^2}\,\left (6\,x+6\,\ln \left (2\right )\right )} \,d x \]
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